A Boeing 747 "Jumbo Jet" has a length of 55.9 m. The runway on which the plane lands intersects another runway. The width of the intersection is 24.0 m. The plane decelerates through the intersection at a rate of 5.61 m/s2 and clears it with a final speed of 43.3 m/s. How much time is needed for the plane to clear the intersection?(Note that the plane enters the intersection when any part of the plane is in the intersection and blocking the other runway. The plane clears the intersection when there is no longer any part of the plane in the intersection blocking the other runway.)
V = 43.3 m/s.
a = -5.61 m/s^2
d = 24 + 55.9 = 79.9 m.
V^2 = Vo^2 + 2a*d = 43.3^2
Vo^2 - 11.22*79.9 = 1874.9
Vo^2 = 1874.9 + 21036 = 22,911
Vo = 151.4 m/s. = Initial velocity.
V = Vo + a*t
V = 43.3 m/s.
Vo = 151.4 m/s.
a = -5.61 m/s^2
Solve for t.
To find the time needed for the plane to clear the intersection, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity of the plane (43.3 m/s)
u = initial velocity of the plane (unknown)
a = acceleration of the plane (-5.61 m/s^2, negative because it's decelerating)
s = distance traveled (55.9 m - 24.0 m = 31.9 m, as the plane clears the intersection)
Rearranging the equation, we get:
u^2 = v^2 - 2as
Now we can substitute the known values and solve for u:
u^2 = (43.3 m/s)^2 - 2(-5.61 m/s^2)(31.9 m)
u^2 = 1870.89 m^2/s^2 + 359.76 m^2/s^2
u^2 = 2230.65 m^2/s^2
Taking the square root of both sides, we find:
u = √2230.65 m/s
u ≈ 47.23 m/s
Now that we have the initial velocity, we can use it to calculate the time needed to clear the intersection. We'll use the equation:
t = (v - u) / a
Plugging in the values, we get:
t = (43.3 m/s - 47.23 m/s) / -5.61 m/s^2
t ≈ -0.70 s
Since time cannot be negative in this context, the negative sign indicates that our assumption of the plane clearing the intersection is incorrect. The plane must still be in the intersection when it reaches a speed of 43.3 m/s.